ON THE EQUILIBRIUM OF A STRATIFIED LAYER OF FLUID

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Abstract
This note demonstrates the equal importance of viscosity and thermal conductivity (or any equivalent process of diffusion) in determining the departure from equilibrium of continuously stratified layers of fluid. The analysis is carried out by an extension of previous variational principles, and is applied to freely bounded horizontal layers which are thermally stratified; the initial rate of growth of small disturbances is shown to depend on the Rayleigh and Prandtl numbers. The method gives the usual critical Rayleigh number for the onset of convection in unstably stratified layers with a linear density gradient, but it also indicates that this critical value of the Rayleigh number suffers little reduction when the stratification is originally non-uniform. Although the analysis is applied to a system which cannot be realized physically, the corresponding results for real systems should be qualitatively similar.

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